Excerpt from the book "Techniques for Geometric Transformation" which is included with "Sacred Geometry Oracle" By John Michale Greer

We live in a time of great transitions. After three centuries in which the Western world has been dominated by the ideology of science, more and more people are taking a hard look at the legacy of the Scientific Revolution, with its dream of a world totally subjected to human reason and its promise of limitless power through technology. The dream and its promise measure up poorly against the hard realities of a spiritually empty, esthetically debased, culturally impoverished, and environmentally devastated world.
In the last fifty years, in response to these concerns, teachings concerning mysticism, magic, divination, and inner development role in modern life. These ancient traditions have proven themselves quite capable of handling the complexities of a postmodern world - more capable, indeed, than many approaches that carry the seal of official scientific approval.
In the modern renaissance of traditional wisdom, through the ancient art of sacred geometry has played a surprisingly small role. At a time when the basic ideas of traditional wisdom are becoming ever more widely known, when everything from astrology to Zen has a ready and increasingly knowledgeable audience, very few people have even encountered sacred geometry.
Much of the problem is simply a matter of how sacred geometry has been presented in modern times. Memories of boring math classes make the whole idea of sacred geometry seem cold, abstract, and difficult to those who have never experienced it, and getting past this barrier has been a slow and difficult process.
With a few stellar exceptions, too, most of the very small handful of recent books on sacred geometry fall short as useful introductions to the art. On the one hand, these books betray a limited and sometimes inaccurate knowledge of the traditional lore. On the other, many of them have a habit of mixing sacred geometry together with a dizzying assortment of speculations about lost continents, ancient astronauts, conspiracy theories, and the like. While I don't intend to pass judgment on such ideas, or to deny them merit on their own terms, it's fair to say that they don't have much to do with traditional sacred geometry; muddling them together with geometrical studies has caused far more confusion than clarity, and done some damage to sacred geometry's reputation besides.
Despite its importance, then, sacred geometry remains the most neglected of the Western world's wisdom teachings. This particularly unfortunate at the present time, for it has things to offer that our modern world desperately needs. It was by way of sacred geometry that ancient architects, artists, designers, and builders created structures and works of art that still astonish the viewer by their beauty, their practicality, and their harmonious relationship to their surroundings. It was by way of sacred geometry that the spiritual and the practical sides of life were woven together seamlessly in the everyday environments of city, town, workplace, and home. In a age when our cities are drowned in soulless ugliness, and our lives are surrounded by objects designed for mechanical efficiency without any human qualities whatsoever, the insights of sacred geometry have much to offer us even on a practical lever.

Understanding Sacred Geometry
Or culture's forgetfulness of sacred geometry extends so far that many people have never heard of it, and some of those who know the term use it in ways the traditional sacred geometers of the past would hardly recognize. Thus, a few paragraphs on matters of definition may be useful here.
The English word "geometry" comes from the Greek geometria, literally "earth measurement" (from ge, "earth," and metron, "measure"). This points back to the ancient origins of geometry, when the art was used to lay out patterns on the earth in order to measure fields and establish the ground plans for sacred structures.
At the time, all geometry was sacred, for two reasons. On the one hand, the Earth itself was understood as a living and holy being, and those who measured it and patterned it recognized their responsibility as mediators between the Earth and the people. Historically we can find echoes of this attitude in the sacred status of boundary stones, in rituals performed at the founding of a city or building of a temple, and in many other traditions that have endured from the distant past. This attitude had much to do with the origins of feng shui in China, and of similar systems, far less well-known, in the Western world and elsewhere.
On the other hand, it was recognized early on that geometry itself offered pathways into the subtle realm of meaning and spirit that we call sacred. The play of geometric form obeys laws that unfold from the nature of experienced reality itself, laws that are not subject to human whims or prejudices. Mastery of those laws provided knowledgeable individuals with tools to reshape the world, both on a physical lever - for geometry was the foundation of much of ancient architecture and technology - and on the subtler levels as well.
Out of this recognition of the sacred possibilities of geometry, an extraordinary tradition of wisdom took shape. It was expressed in many different forms in the cultures that treasured it; the forgotten geometers who planned and built the mighty stone circles of northwestern Europe no doubt understood geometry in very different ways from the temple priests of Egypt, the initiates of the Pythagorean Brotherhood of ancient Greece, the Taoist sages of China, or the master builders of medieval Europe. Their work varied equally; it takes different methods and somewhat different skills to trace out the design of a stone circle, to erect a Gothic cathedral, to work out the proportions of a Renaissance painting, or to teach a new initiate to apply geometric principles of balance and harmony to his or her own daily life.
Still, a common thread of insight runs through all of these expressions of sacred geometry tradition. All of them recognized the need to join geometric theory with its expression in practice. All of them knew how to fuse spirit, form, and matter into unity through the practice of their art. All of them recognized that beauty and meaning come from the presence of the living spirit in form and matter, and all of them saw clearly that this comes through the creative mind from beyond, not from the individual ego and its manipulations.
These insights, however, did not remain central to geometric practice. As societies grew more complex and human activities more specialized, the practical side of geometry grew away from its roots in the living spirit. This was a slow process, and by no means a continuous one. While there are records of purely practical geometry from ancient Egyptian times, there were still times and places thereafter when the practical and spiritual sides of geometry were reunited, giving rise to soaring works of human genius, such as the temples of classical Greece and Gothic cathedrals of medieval Europe.
Only with the end of the Renaissance and the coming of the Scientific Revolution did the break become total. It's not an accident that the term "sacred geometry" came into being after this point. Only when the main current of geometry in the West lost the last of its connections to the sacred was it necessary to create a new phrase, "sacred geometry," to refer to what all geometry had once been.
We can define sacred geometry, then, as the part of using geometric forms as a gate way to the knowledge and presence of the living spirit. If your only contact with geometry has been with the sort that's taught in public schools, in other words, the approach on which the Sacred Geometry Oracle is based may seem pretty strange. The emblems and exercises in this book, and in other books of traditional sacred geometry , have nothing to do with proving theorems or calculating the sides of triangles! Instead, sacred geometry is about opening up the self to the experience of geometric form, recognizing the presence of underlying laws in the play of form, and learning to understand the universe in a different and deeper way.
Geometry was only one of a group of ancient arts with the same broad purpose and approach, and most of the cultures that made use of sacred geometry drew on these other arts as well. In the Western world, from Greek times to the end of the Renaissance, these arts were united as the "quadrivium" or "Four Ways" of arithmetic, geometry, music, and astronomy.
All of these, it has to be remembered, were studied and practiced as sacred disciplines. Nowadays, we might use different names to better communicate what the branches of the quadrivium were about: numerology, the spiritual science of number; sacred geometry, the spiritual science of form; harmonics, which embraces not only the inner dimensions of music, but also the whole realm of relationship and proportion; and calendrics, the spiritual science of the cycles of time. All these interact in complex ways; some of those interactions will be explored later on in this book.

Excerpt from the book "Techniques for Geometric Transformation" which is included with "Sacred Geometry Oracle" By John Michale Greer